Renormalization-group investigation of the S=1 random antiferromagnetic Heisenberg Chain

TL;DR

This paper develops and compares perturbative and non-perturbative renormalization-group methods to analyze the phase diagram of the S=1 random antiferromagnetic Heisenberg chain, confirming results with existing numerical techniques.

Contribution

It introduces variants of the Ma-Dasgupta RG approach, including a non-perturbative method, and applies them to the S=1 chain to produce consistent phase diagrams.

Findings

Both methods agree on the disorder-dependent phase diagram.

The phase diagram matches density-matrix renormalization-group results.

The non-perturbative approach preserves the lowest gaps exactly.

Abstract

We introduce variants of the Ma-Dasgupta renormalization-group approach for random quantum spin chains, in which the energy-scale is reduced by decimation built on either perturbative or non-perturbative principles. In one non-perturbative version of the method, we require the exact invariance of the lowest gaps, while in a second class of perturbative Ma-Dasgupta techniques, different decimation rules are utilized. For the S=1 random antiferromagnetic Heisenberg chain, both type of methods provide the same type of disorder dependent phase diagram, which is in agreement with density-matrix renormalization-group calculations and previous studies.